The limitations of Lenz law?

What are the limitations of Lenz law? If there where none, you could just move a magnet through a coil and keep moving it away, thus creating the worlds most powerful magnet. This seems highly unlikely.

When moving a magnet towards the coil, the external magnet field induces a current in the coil, creating its own internal magnet field with the same magnetude but with the opposite direction, thus negating the change.

When the magnet moves through and out on the other side of the coil, the current changes direction (?) and the internal magnetfield is increased in the same direction as the outer magnet field is, thus negating the change again.

Does the internal magnet field increase until the magnet is too far away from the coil to be able to generate the current and as a result, the internal magnetfield?